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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 329, page id 1815201908:0386
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pledo
e
AC,
CCHI
EL L TPSTS.
22
OcCurrences AC linex in LTHI, e circulo ABC in II: Fancq rectis CF
aequaleslince C L.
Dicopuncta A L. L. esse ad cllipsim.
Demonstratio.
VCanTIE Ex C per C lineX CGK. ve
ROC rectangulum est ad rectangulum
KGC, siC = FC F. rectangulum est ad rectan.
culum LiCtRi sed eAbrEKC C rectangulum
ad rectangulum RCC, sic OH linca ad li.
neam CIB, _ VE FCF rectangulum ad rc-
ctangulum FOF, SIC FC linea ad lincam
FC, igitur ve GHI ad GFI, siC F C ad F C3
id est L. C ad IC, e componendo permuran-
do L. HIad I. HP, vrC HI adCHI. Ouare pun.
aa ALL. sunc ad ellipsim.
PROPOSITIO CLZI.
VIE ABC ellipsis diameter quaecuin-
 que AB, actilque per A lincis C D,
que cllipli OcCUEraHE in C C, AaEVEAC
ad AC, siC AD ad AD, _ VE AC ad AD, sic AB ad AP.
Dico puncta A, D; F ad eandem elliplim elso.
Demonstratio.
e cua
Votam eh e l palalteta ClansaGC
Lproinde LC A, DC A lmilia, crunc ve linCa
C a ad lincas AD Cinsulae ad Cingulas, ica singula
FC ad singulas CD. Aequi singul_ C A CuHE 2d
singulas AD VeB A ad AF. EroOsingula FC sunt
ad singulas DO, VE B A ad AF. Ouare quam FA-
tionem habet vna FC ad inam DC, candem ha-
benesinoulx reliquae F C ad singulas reliquas DC.
lgicur permucando velune F C 2d FC, ita CD PunE
ad DC, ddcoguere lune quadrara FC ad quadraca
F C, ica quadrata ED sunead quadraca OD. limili-
ter demonstrabimus, VE A F sUnE ad A F, AC eNC AG
2d A9. Vnde vereliguae FB sune ad reliquas F B,
ica reliquae G P. sunc ad reliquas OF. O uare cumre-
etangula AFB racionem habeane ad lele invicem
compolicam exracionibus AB ad AF, _ F B, ad F B.
quae ostenla lunc eadem esse rarionibus AC ad AC,
_ GF, ad OD, ex quibus componicur racio rectan-
sulorum AOF; erunc ve rectangula AFB ad rectangula AF B. Ic rectangula
AC Pi adrectangula AO B. Arqui rectangula AFB sunc adrectangula AFB, VE
quadtaca FC ad quadrara F C, hoc est per luperius demonstraca, ve quadrata CD
ad quadrata GDs ergo rectangula AC F sune ad recrangula AG F, ve quadraca
CD ad quadcaca CD. Puncca isicur D A, AD F sunc ad ellipsim. Oyod exac
demonstrandums